Fundamental to the performance of any control algorithm, is its servo-regulatory ability. That is, changes in the set-point should be tracked quickly and smoothly and the controlled variable should be kept at or near its set-point despite unmeasured disturbances affecting the process. In addition the controller should maintain stability and acceptable control performance in the face of structural and/or parametric uncertainty. In certain applications the cost of providing effective control is also a significant factor. While most multivariable control laws utilize some form of cost minimization, the costs typically reflect control movement rather than actual costs. The invention described in this patent teaches a scheme that is based on minimizing costs while still providing effective control. The nonlinear cost functions used in defining the control sequence can be stated to reflect either actual operating costs (dollars) or auxiliary costs (efficiency, quality, etc.) Cost minimization is predicated on the assumption that there are more manipulated variables than controlled variables. Thus it is up to the controller to allocate the correct blend of the manipulated variables such that both control and cost objectives are met. The control scheme described herein was designed specifically to address these basic criteria.
A predictive control law provides the fundamental structure for the new controller. The adaptive controller utilizes a receding horizon formulation. The receding horizon formulation can be used for multivariable control with or without cost minimization. It can also be used for robust univariate servo-regulatory control. Predictive control in and of itself is by no means new. Indeed predictive control is the central theme behind the benchmark works of Cutler and Ramaker in their Dynamic Matrix Control (DMC) algorithm (Cutler, C. R., and B. L. Ramaker, "Dynamic Matrix Control--A Computer Control Algorithm," Joint Automatic Controls Concerence Proceedings, San Francisco (1980)) and Richalet et. al. in their Model Algorithmic Control (MAC) algorithm (Richalet, J. A., A. Rault, J. D. Testud, and J. Papon,, "Model Predictive Heuristic Control: Application to Industrial Processes," Automatica 14, 413 (1978)).
Much of the current control work reported in the literature today is based in some degree on these approaches. Horizon based prediction and control has also been described and implemented in the past (Tung, L. S., "Sequential Predictive Control of Industrial Processes," Proc. ACC, San Francisco (1983); Ydstie, B. E., L. S. Kershenbaum, and R. W. H. Sargent, "Theory and Application of an Extended Horizon Controller," AlChE J., 31, 771 (1985); and Lee, K. S., and W. K. Lee, "Extended Discrete Time Multivariable Adaptive Control Using Long Term Predictor," Int. J. Control, 38, 495 (1983)). The unique aspects of the new control law described herein are that it combines the attractive features of DMC and horizon control and eliminates the inherent disadvantages of the original formulations.
In DMC there is no direct mechanism to tune the controller. In addition the size of the matrix to be inverted at each control update is specified by the number of input terms used in the prediction. These deficiencies which cause considerable practical difficulties in implementing a controller based on such strategies can be eliminated by using a horizon formulation. Unfortunately, previously known horizon based techniques do not eliminate the impracticalities since the number of terms that need to be estimated by the identifier depend on the horizon window. For many uses this can be computationally too burdensome to be acceptable. In the new formulation, a horizon based technique is utilized where the prediction is accomplished using an auto-regressive moving average (ARMA) model in a recursive fashion. In addition, the controller using the new control law described herein allows for the direct imposition of constraints on both process and control outputs at the end of the horizon window.
Use of optimization strategies in plant operation is also not a new concept. Many optimization techniques are global strategies that determine appropriate allocation levels among competing resources. Typically the global approaches do not take into account transient performance at the regulatory level. In a recent patent (U.S. Pat. No. 4,873,649) Grald and MacArthur teach an on-line method for control of vapor compression space conditioning equipment such that COP (coefficient of performance) is optimized. The optimization technique however does not deal directly with transient response and hence satisfactory servo-regulatory performance can not be insured. Morshedi et al (Morshedi, A. M., C. R. Cutler, and T. A. Skrovanek, "Optimal Solution of Dynamic Matrix Control with Quadratic Programming Techniques (QDMC)," Proc. ISA, Part 1, 40 (1985)) describe a pseudostatic approach for incorporating cost into the control design. In their formulation the manipulated variables in question are assigned pseudo set-points which are determined by solving a static linear optimization subproblem for the final value of the inputs. The nominal inputs are then treated as controlled variables with their set-points given by the computed values of the steady state inputs. The conventional control strategy is then augmented to reflect this additional information.
In the controller described in the instant patent, a technique for coupling dynamic nonlinear cost minimization with uncompromised servo-regulatory response is accomplished for the first time. While cost minimization is a desirable option of the controller, robust servo-regulatory performance is still the fundamental objective. To this end one simple form of the controller uses a multivariable feedforward/feedback algorithm. Feedforward compensation offers the potential for improved control performance since it allows the controller to react before a measurable disturbance has a chance to affect the response of the plant. In addition, as will be described later, it provides the mechanism for coupling the cost minimization to the desired servo-regulatory response.
To be effective, the controller requires an internal model that relates all controller outputs and measurable disturbances to all process outputs. (The process outputs are the outputs of the plant as indicated by sensing means located proximate thereto.) The parameters of this internal model are determined on-line by measuring the system response to the controller outputs over time, and provide the adaptive ability of the controller. Evaluation of the unknown model coefficients for each process output is accomplished by a recursive least squares (RLS) estimate. Other standard techniques may be used to accomplish this model identification and are well known.
While techniques for model identification are well known, insufficient excitation or inappropriate sample rate selection will render the identification inaccurate. The invention described in this patent teaches a method for automatically determining the correct control and identification sample rate. In addition, a technique is given for automatically selecting the horizon window and for adjusting the control algorithm when excitation is insufficient for accurate model identification.